Starnes, The Practice of Statistics, 6e, Chapter 5

probability

A number between 0 and 1 that describes the proportion of times an outcome of a chance process would occur in a very long series of repetitions. (p. 301)

law of large numbers

If we observe more and more repetitions of any chance process, the proportion of times that a specific outcome occurs approaches a single value, which we call the probability of that outcome. (p. 301)

simulation

Imitation of chance behavior, based on a model that accurately reflects the situation. (p. 304)

probability model

Description of some chance process that consists of two parts: a sample space S that lists all possible outcomes and a probability for each outcome. (p. 314)

sample space

Set of all possible outcomes of a chance process. (p. 314)

event

Any collection of outcomes from some chance process. An event is a subset of the sample space. Events are usually designated by capital letters, like A, B, C, and so on. (p. 315)

complement

The complement of event A, written as AC, is the event that A does not occur. (p. 316)

complement rule

The probability that an event does not occur is 1 minus the probability that the event does occur. In symbols, P(Ac) = 1 - P(A). (p. 316)

mutually exclusive

Two events A and B that have no outcomes in common and so can never occur together. That is, P(A and B) = 0. (p. 317)

addition rule for mutually exclusive events

If A and B are mutually exclusive events, P(A or B) = P(A) + P(B). (p. 317)

general addition rule

If A and B are two events resulting from a chance process, then the probability that event A or event B (or both) occur is P(A or B) = P(A ∪ B) = P(A) + P(B) - P(A ∩ B). (p. 320)

Venn diagrams

A diagram that consists of one or more circles surrounded by a rectangle. Each circle represents an event. The region inside the rectangle represents the sample space of the chance process. (p. 322)

intersection

The event "A and B" is called the intersection of events A and B. It consists of all outcomes that are common to both events, as is denoted by A ∩ B. (p. 323)

union

The union of events A and B, denoted by A ∪ B, consists of all outcomes in A or B or both. (p. 323)

conditional probability

Probability that one event happens given that another event is already known to have happened. (p. 331)

independent events

Two events are independent if the occurrence of one event does not change the probability that the other event will happen. (p. 335)

general multiplication rule

The probability that events A and B both occur can be found using the formula P(A ∩ B) = P(A) · P(B|A) where P(B|A) is the conditional probability that event B occurs given that event A has already occurred. (p. 338)

tree diagram

A diagram that shows the sample space of a chance process involving multiple stages. The probability of each outcome is shown on the corresponding branch of the tree. (p. 339)

multiplication rule for independent events

If A and B are independent events, then the probability that A and B both occur is P(A ∩ B) = P(A) · P(B). (p. 344)